Although most girls are all just the same not every girl responds to the same comunication method..
Say she's actually being honest and she was busy, she's got many friends and has a really active social life. She doesn't need you' she's just bored and starts texting you to feel desired and chased after.
I told you once, she craves attention son DO NOT GIVE HER ANY, do not ask her out. EVER.
THe girl is being a bitch and she knows it and she thinks she can play with you.
By asking her out you yield all the power you have. DO not do that. She's over the line and you should either consider this 3 options I present to you:
1. Freeze her out for 2 weeks.. IF she texts you just politely reply and say you're bussy. If you're on SPAM, constantly change your profile picture and loggin several times during the day just so she can check out your last loggin times. You'll drive her jealous just thinking that you're not so busy to chat with other people... Get what I'm saying? After 1 or 2 weeks text her friendly manner and just chat, be funny, not resentful, talk and talk and make her be interested in ASKING YOU OUT. WARNING, this might cause you to loose her completely cuz many girls are really resentful when being treated like that.. This is YOU ATTRACTING HER AND MAKING HER invite you not you invite her. Also this is the less needy way of making things happen.
2. Be Straig forward with her and text her something like: "Hey, you know, It's been a long time that we've been chatting/texting etc.. and we haven't had the chance to actually meet again since last time.. I kinda want to see ya again cuz we have fun together. I'll be free on Saturday (any day you feel) after i finish doing some work at home/office/whatever, what about you? Are you in? WARNING. This is a very straight forward approach. It makes her see you as an honest, sensitive, ballsy dude who's not afraid to speak his feelings/mind... Many girls respond good to this approach. BUT, in case she says she's busy and she doesn't make a counter offer (e.g. Im bussy saturday but lets make it sunday)... It will be your turn just to walk away. Think of it this way. IF YOU ARE ALFA MALE, you cannot waste time on flaky people, even if she's hot. You're a man of options, right? If she doesn't make a counter offer just leave it like that, say "its ok, well meet other time then, and never text her again.."
3. LOOSE HER NUMBER. I Know This is not the "Loose her number forum"... but this follow what my principle is and what I live by: GAME more than 3 girls simultaneously. I know, I Know, its about quality not quantity, but you can't have 1 single girl hinder your progress in the world of pickup.. Being weeks/days now with all that flakyness all her irresponsiveness... Besides, having other girls in line paying you attention puts you in a much better state of mind than just being waiting entire weeks for one girl to reply to your text..
In my opinion, try any of those, but be consistent and congruent with whatever road you decide to take. And one more thing.. Whatever you decide with this particular female, try gaming other girls too!

you'll learn more, faster and a wider variety of things.. With this one girl you are just learning your way around irresponsiveness and flakyness and that's it. It's cool learning though, but I see much more potential in you.

OH one more thing...
Do not mind the results with a particular girl. Enjoy gaming, enjoy learning, and if you fuck it up, SO WHAT?! There are plenty of fish in the sea